The halo-stellar mass relation is shown in comparison with other theoretical results, derived from high resolution zoom-in hydrodynamic simulations (, , , , , , ), and large-box simulations in which best-fits are provided ( (solid line),  (dotted line)). Our \(\rm M_{\rm vir}\) -\(\rm M_{\ast }\)  relation, in particular, appears to be in line with the fit suggested by  (dashed line), whose result is based on the abundance matching approach. We should, however, caution that the effect of photoionization heating from local sources such as individual Pop III stars and Pop II clusters is not considered in this work. The impact of radiative feedback by local sources is still under debate. A recent study by  has shown that the stellar mass of small galaxies (\(M_{\rm vir}=2.4\times 10^9 {\,M_\odot }\) ) is predominantly determined by the external UVB, but that the effect of local sources is insignificant. [1]}, on the other hand, have demonstrated that the photoionization heating by stars could lower the stellar mass by a factor of \(5-10\)  for dwarf galaxies with a mass of \(M_{\rm vir}=10^9 {\,M_\odot }\) . This discrepancy is likely due to the difference in the detailed prescription for sub-grid models and resolution.
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